How do you factor $x^{2} - 15 x + 50$ $x^2-15x+50$ ?

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How do you factor $x^{2} - 15 x + 50$ $x^2-15x+50$ ?

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Answer 1 · 2015-05-22T07:09:50

$x^{2} - 15 x + 50$ $x^2-15x+50$

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 50 = 50$ $N_1*N_2 = a*c = 1*50 = 50$
and
$N_{1} + N_{2} = b = - 15$ $N_1 +N_2 = b = -15$

After trying out a few numbers we get $N_{1} = - 5$ $N_1 = -5$ and $N_{2} = - 10$ $N_2 =-10$
$(- 5) \cdot (- 10) = 50$ $(-5)*(-10) = 50$ , and $(- 5) + (- 10) = - 15$ $(-5)+(-10)= -15$

$x^{2} - 15 x + 50 = x^{2} - 5 x - 10 x + 50$ $x^2-15x+50 = x^2-5x - 10x +50$

$= x (x - 5) - 10 (x - 5)$ $= x(x-5) -10(x-5)$
$= (x - 10) (x - 5)$ $= (x-10)(x-5)$ , this is the factorised form.

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How do you factor $x^{2} - 15 x + 50$ $x^2-15x+50$ ?

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